Details

Time bar (total: 59.1s)

sample361.0ms

Algorithm
intervals
Results
211.0ms106×body1280valid
61.0ms71×body640valid
58.0ms21×body2560valid
12.0ms17×body320valid
6.0ms31×body80valid
4.0ms10×body160valid

simplify8.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
8.0ms
(- (tan (+ x eps)) (tan x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize26.0ms

Local error

Found 2 expressions with local error:

2.8b
(tan (+ x eps))
1.1b
(- (tan (+ x eps)) (tan x))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity tan-quot add-log-exp
2×pow1 tan-sum add-cbrt-cube add-exp-log frac-sub add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
Slowest
26.0ms
(- (tan (+ x eps)) (tan x))
9.0ms
(tan (+ x eps))

series235.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
132.0ms
(- (tan (+ x eps)) (tan x))
104.0ms
(tan (+ x eps))

simplify1.3s

Counts
15 → 33
Calls
15 calls:
Slowest
440.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
398.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
159.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
136.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
41.0ms
(- (* (sin (+ x eps)) (cos x)) (* (cos (+ x eps)) (sin x)))

prune379.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.1b

localize45.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1
5×distribute-lft-out
4×insert-posit16 associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×flip3-+ flip3-- frac-add associate-/r/ flip-+ flip-- difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
99.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
44.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
25.0ms
(* (tan x) (tan eps))
8.0ms
(+ (tan x) (tan eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
480.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
280.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
146.0ms
(* (tan x) (tan eps))
125.0ms
(+ (tan x) (tan eps))

simplify5.5s

Counts
74 → 102
Calls
74 calls:
Slowest
513.0ms
(/ (* (* (+ (tan x) (tan eps)) (+ (tan x) (tan eps))) (+ (tan x) (tan eps))) (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))))
472.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
431.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
381.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
301.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.0b

localize39.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))
0.6b
(cbrt (tan x))
0.6b
(cbrt (tan x))
0.6b
(cbrt (tan x))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×cbrt-prod *-un-lft-identity
7×add-cube-cbrt
6×add-log-exp
4×pow1 add-cbrt-cube tan-quot add-exp-log insert-posit16
3×cbrt-div pow1/3
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log frac-sub flip-- distribute-lft-out--
Counts
4 → 56
Calls
4 calls:
Slowest
103.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))
3.0ms
(cbrt (tan x))
3.0ms
(cbrt (tan x))
3.0ms
(cbrt (tan x))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
517.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps))))) (tan x))
188.0ms
(cbrt (tan x))
155.0ms
(cbrt (tan x))
145.0ms
(cbrt (tan x))

simplify3.0s

Counts
32 → 68
Calls
32 calls:
Slowest
366.0ms
(* (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps)))) (cos x))
252.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
250.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (tan eps)))) (sin x)))
246.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
236.0ms
(+ (* 1/9 (pow (pow x 7) 1/3)) (+ (* 13/405 (pow (pow x 13) 1/3)) (pow x 1/3)))

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.0b

localize39.0ms

Local error

Found 4 expressions with local error:

6.0b
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
0.3b
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
0.2b
(* (tan x) (tan eps))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
123×times-frac
104×*-un-lft-identity
83×add-sqr-sqrt
67×add-cube-cbrt
23×associate-/r*
19×add-exp-log
16×associate-/r/ distribute-lft-out
15×tan-quot
13×add-cbrt-cube
8×div-exp
7×pow1 div-inv
6×associate-/l* add-log-exp
5×flip3-+ frac-add flip-+ difference-of-squares
4×cbrt-undiv insert-posit16
3×associate-*r* associate-*l*
2×rec-exp clear-num frac-2neg flip3-- 1-exp flip-- distribute-lft-out-- associate-/l/
1×frac-times sub-neg diff-log div-sub pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod pow-flip inv-pow unswap-sqr
Counts
4 → 182
Calls
4 calls:
Slowest
101.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
27.0ms
(* (tan x) (tan eps))
19.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
16.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
520.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
354.0ms
(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
333.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
141.0ms
(* (tan x) (tan eps))

simplify24.1s

Counts
222 → 194
Calls
222 calls:
Slowest
671.0ms
(/ (* (* 1 1) 1) (* (* (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))) (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))))
493.0ms
(/ (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))) (* (* (+ (tan x) (tan eps)) (+ (tan x) (tan eps))) (+ (tan x) (tan eps))))
478.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
412.0ms
(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (pow (tan x) 3) (pow (tan eps) 3))))
384.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.0b

regimes304.0ms

Accuracy

89% (0.8b remaining)

Error of 15.2b against oracle of 14.3b and baseline of 21.9b

bsearch390.0ms

end0.0ms

sample15.2s

Algorithm
intervals
Results
7.5s3236×body1280valid
3.2s616×body2560valid
3.0s1967×body640valid
696.0ms767×body320valid
337.0ms1070×body80valid
213.0ms344×body160valid